Quadrature amplitude modulation (QAM) is a particular type of modulation scheme that can be used to transmit digital data by modulating a carrier signal. QAM “symbols” are mapped to binary data bits based on the amplitude and phase of the QAM signal received during a particular symbol period. The mapping and de-mapping of QAM symbols is typically performed using a “constellation,” wherein each point on the constellation represents both a QAM symbol (e.g., corresponding to a set of amplitude and phase information) and a binary bit pattern (e.g., corresponding to a set of labeling bits). Thus, a constellation may be used to map binary data bits to QAM symbols to be transmitted, as well as to recover (e.g., de-map) binary data from received QAM symbols. For example, an M-QAM constellation may be used to map M number of symbols to M number of bit patterns, wherein each bit pattern includes L=log2(M) number of labeling bits.
The data rate of a QAM communications system varies directly with the QAM constellation size. For example, increasing the number of constellation points (M) also increases the number of data bits (L) that can be communicated during a symbol period (e.g., L=log2(M)). As the constellation becomes more densely populated, the spacing between constellation points (e.g., the “Euclidean distance”) becomes smaller. This reduces the margin of error that the system can tolerate when using the constellation to recover data bits from a received QAM signal. Further, because imperfections exist in the transmission channel and in the receiving circuits, the received signal may be distorted (e.g., in shape). This may cause bit errors in the received signal.